notes of quantum mechanics

1. Quantum Mechanics
Breakdown of Classical Concepts and
Old Quantum Theory
Written By: Shahzada Khan
Institute of Physics
University of Sindh Jamshoro

2. Statement: When ultraviolet light falls on a metal surface, electrons are given out which are called
photoelectrons and process is called Photoelectric Effect. Or the energies of electrons liberated by
light depends on the frequency of the light.
 EXPERIMENT STUDY OF PHOTOELECTRIC EFFECT: The experiment arrangement
consists of an evacuated glass tube in which two metal electrodes E and C are sealed. The two
electrodes are connected to two terminals of a battery through an ammeter and voltmeter.
 The plate E which is connected to negative terminal is called emitter and the plate C which is
connected to positive terminal is called collector. When light is made to fall on E, the electrons
are given out. These electrons are accelerated towards plate C and ammeter shows current. If
light is switched off, ammeter shows no current.
 The potential difference between emitter and collector is not same as the potential
difference V supplied by external battery and read on voltmeter. There is also a second emf
associated with fact that the emitter and collector are almost always made of different
materials. If suitable precautions are taken, the contact potential difference remains constant
through the experiment. The potential difference V is sum of these tow potentials i.e
 We can find maximum kinetic energy of photoelectrons by reversing the polarity of plate E
and C.
PHOTOELECTRIC EFFECT
ext cpdv v v 
cpdv
extv

3.  EXPERIMENT RESULTS: Above experiment was performed by using lights of different
intensity and frequency and following results were obtained:
1. No photoelectrons are emitted; however, intense the light may be, if the frequency of light
is smaller than a critical value , called threshold frequency.
2. Threshold frequency depends upon nature of material used as an emitter.
3. The maximum energy of photoelectrons increase with increasing frequency above threshold
frequency.
4. The photoelectrons are emitted instantaneously even when the weakest possible beam of
light having frequency above falls on emitter.
5. The energy of photoelectrons does not depend upon the frequency of light.
6. The number of photoelectrons emitted from emitter is proportional to intensity of light.
7. The kinetic energy of such energy packets is given by this formula.
2
max 0
1
.
2
K E mv v e 
0
0

4. 1. The emission or absorption of energy (in the form of radiation) by a body is not a
continuous process.
2. The emission or absorption of radiation takes places in the form of wave packets called
Quanta. In case of light, this quanta of energy is called Photon.
3. The amount of energy associated with a Quanta of radiation is proportional to the frequency
of radiation.
4. …………………(1)
Where “h” is Plank’s constant and its values is , and “v” is the frequency.
1. Frequency is inversely related is wavelength( )
2. Putting values of in equation “1”
QUANTUM THEORY OF LIGHT or PLANK’S QUANTUM THEORY:
In 1900, Max Plank proposed Quantum Theory of Radiation.
34
6.63 10 .h J s
 
E
E h

1


c




hc
E

 hc
E



5.  EINSTEIN’S EQUATION FOR PHOTOELECTRIC EFFECT
 Statement: Einstein’s equation is based upon Plank quantum theory. According to him,
emission or absorption of radiation is not a continuous process but it takes place in form of
small packets of energy called photons. The energy of each photo is proportional to frequency
i.e
 Where , called Plank’s constant.
 Explanation: Einstein used above theory to explain photoelectric effect. When light in form
of photon fall on metal surface, then each photon transfers its energy to electrons. The
minimum kinetic energy required by an electron to come out of metal surface is called Work
function, denoted by .
 , is threshold frequency.
 If incident light has its frequency less than threshold frequency, no photoelectric effect takes
place. On the other hand if incident light has its frequency greater than threshold frequency, the
struck electrons utilize the gained energy in two forms: one part of his energy is used in form
of work function and remaining energy appears in form of maximum kinetic energy to
overcome the retarding potential difference between emitter and collector. If “hv” is energy of
each photon, is work function and is maximum kinetic energy, then
 This equation is known as Einstein equation of photoelectric effect.
E
E h
34
6.63 10 .h J s
 
0h  0
 max 0K V e
2
0
1
2
h h mv  
maxh K  
maxK h  
oV e h   oV e h  

7. De-Broglie Wave
Statement:“A moving body behaves in certain ways as though it has a wave nature.”
 Explanation: Louis De Broglie in 1924 put forward the suggestion that matter has dual nature
like light or x-rays radiation and therefore behaves like discrete particle and waves. The waves
associated with matter in motion are called matter waves or De-Broglie waves. The
wavelength of the waves accompanied by a particle of material in motion is called De-Broglie
wavelength.
 DERIVATION OF DE-BROGLIE WAVELENGTH
Method (A)
A photon of light of frequency “ ” has the
momentum
Which can be expressed in terms of
wavelength “ ” as
Since
The wavelength of a photon is therefore
specified by its momentum according to the
relation
Method (B)
If the frequency of a photon is denoted by (E)
then
Since
Putting this value in above equation.
If “m” denoted the mass of the photon, then
Comparing equation “1” and “2”
If particle is electron, then

h
p
c



h
p


c  1
c



h
p
  h
mv
 
E h
c 
c



hc
E

 ………(1)
2
E mc ………(2)
2 hc
mc


h
mc
 
h
mv
 